2/w-5=1/3w

Solution for 2/w-5=1/3w equation:

2/w-5=1/3w

We move all terms to the left:

2/w-5-(1/3w)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/w-(+1/3w)-5=0

We get rid of parentheses

2/w-1/3w-5=0

We calculate fractions


6w/3w^2+(-w)/3w^2-5=0

We add all the numbers together, and all the variables

6w/3w^2+(-1w)/3w^2-5=0

We multiply all the terms by the denominator


6w+(-1w)-5*3w^2=0

Wy multiply elements

-15w^2+6w+(-1w)=0

We get rid of parentheses

-15w^2+6w-1w=0

We add all the numbers together, and all the variables

-15w^2+5w=0

a = -15; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-15)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-15}=\frac{-10}{-30}
=1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-15}=\frac{0}{-30}
=0
$